Solve 1/2x+1/3+1/6=4

$$\frac { 1 } { 2 } x + \frac { 1 } { 3 } + \frac { 1 } { 6 } = 4$$

Solve for x

$$x=7$$

Steps for Solving Linear Equation

Least common multiple of 3 and 6 is 6. Convert \frac{1}{3} and \frac{1}{6} to fractions with denominator 6.

$$\frac{1}{2}x+\frac{2}{6}+\frac{1}{6}=4$$

Since \frac{2}{6} and \frac{1}{6} have the same denominator, add them by adding their numerators.

$$\frac{1}{2}x+\frac{2+1}{6}=4$$

Add 2 and 1 to get 3.

$$\frac{1}{2}x+\frac{3}{6}=4$$

Reduce the fraction \frac{3}{6} to lowest terms by extracting and canceling out 3.

$$\frac{1}{2}x+\frac{1}{2}=4$$

Subtract \frac{1}{2} from both sides.

$$\frac{1}{2}x=4-\frac{1}{2}$$

Convert 4 to fraction \frac{8}{2}.

$$\frac{1}{2}x=\frac{8}{2}-\frac{1}{2}$$

Since \frac{8}{2} and \frac{1}{2} have the same denominator, subtract them by subtracting their numerators.

$$\frac{1}{2}x=\frac{8-1}{2}$$

Subtract 1 from 8 to get 7.

$$\frac{1}{2}x=\frac{7}{2}$$

Multiply both sides by 2, the reciprocal of \frac{1}{2}.

$$x=\frac{7}{2}\times 2$$

Cancel out 2 and 2.

$$x=7$$